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The effects of spatial heterogeneity on the dynamics of reaction-diffusion models have been studied extensively. In particular, global dynamics of general spatially heterogeneous (but temporally static) Lotka–Volterra competition-diffusion systems were completely clarified by He and Ni in 2016. However, the evolutionary impacts of temporal periodicity combined with spatial heterogeneity in population ecology remain a challenging issue. In this work, we consider a population model of two competing species in a both spatially varying and temporally periodic environment, where the two species only differ in their random dispersal rates but are otherwise ecologically identical. In a pioneering 2001 work on this model by Hutson et al., by constructing various choices of resource functions and dispersal rates of the two species, the authors demonstrated that all the following three types of dynamics are possible: (i) stable coexistence of the two species; (ii) the slower diffuser invades the faster one but not vice versa; (iii) the faster diffuser invades the slower one but not vice versa. This is in drastic contrast with the spatially heterogeneous but temporally static case, where Dockery et al. showed in 1998 that the slower diffuser always wipes out the faster one. In this paper, we completely and explicitly characterize the asymptotic stability of both semitrivial periodic solutions in terms of the two dispersal rates and the resource function, when either dispersal rate is sufficiently small or large. In particular, the direction of selection on the dispersal rate during the evolution can be elucidated in these instances. Some novel analytical methods are developed to investigate asymptotic behaviors of the underlying time-periodic parabolic eigenvalue problem and its adjoint problem. We hope that these methods are of independent interest in the area of time-periodic parabolic equations. [ABSTRACT FROM AUTHOR]

In extending Stein's method to new target distributions, the first step is to find a Stein operator that suitably characterises the target distribution. In this paper, we introduce a widely applicable technique for proving sufficiency of these Stein characterisations, which can be applied when the Stein operators are linear differential operators with polynomial coefficients. The approach involves performing an asymptotic analysis to prove that only one characteristic function satisfies a certain differential equation associated to the Stein characterisation. We use this approach to prove that all Stein operators with linear coefficients characterise their target distribution, and verify on a case-by-case basis that all polynomial Stein operators in the literature with coefficients of degree at most two are characterising. For X denoting a standard Gaussian random variable and Hp the p-th Hermite polynomial, we also prove, amongst other examples, that the Stein operators for Hp(X), p = 3; 4;: ::; 8, with coefficients of minimal possible degree characterise their target distribution, and that the Stein operators for the products of p = 3; 4;: ::; 8 independent standard Gaussian random variables are characterising (in both settings the Stein operators for the cases p = 1; 2 are already known to be characterising). We leverage our Stein characterisations of H3(X) and H4(X) to derive characterisations of these target distributions in terms of iterated Gamma operators from Malliavin calculus, that are natural in the context of the Malliavin-Stein method. [ABSTRACT FROM AUTHOR]

We prove some qualitative properties for singular solutions to a class of strongly coupled system involving a Grossâ€"Pitaevskii-type nonlinearity. Our main theorems are vectorial fourth order counterparts of the classical results due to Serrin (1964 Acta Math. 111 247â€"252), Lions (1980 J. Differ. Equ. 38 441â€"450), Aviles (1987 Commun. Math. Phys. 108 177â€"192), and Gidas and Spruck (1981 Commun. Pure Appl. Math. 34 525â€"598). On the technical level, we use the moving sphere method to classify the limit blow-up solutions to our system. Besides, applying asymptotic analysis, we show that these solutions are indeed the local models near the isolated singularity. We also introduce a new fourth order nonautonomous Pohozaev functional, whose monotonicity properties yield improvement for the asymptotics results due to Soranzo (1997 Potential Anal. 6 57â€"85). [ABSTRACT FROM AUTHOR]

This paper presents asymptotic formulas in the case of the following two problems for the Pucci's extremal operators M ± . It is considered the solution u ε (x) of − ε 2 M ± ∇ 2 u ε + u ε = 0 in Ω such that u ε = 1 on Γ. Here, Ω ⊂ R N is a domain (not necessarily bounded) and Γ is its boundary. It is also considered v (x , t) the solution of v t − M ± ∇ 2 v = 0 in Ω × (0 , ∞) , v = 1 on Γ × (0 , ∞) and v = 0 on Ω × { 0 }. In the spirit of their previous works [Berti D, Magnanini R. Asymptotics for the resolvent equation associated to the game-theoretic p-laplacian. Appl Anal. 2019;98(10):1827–1842.; Berti D, Magnanini R. Short-time behavior for game-theoretic p-caloric functions. J Math Pures Appl (9). 2019;(126):249–272.], the authors establish the profiles as ϵ or t → 0 + of the values of u ε (x) and v (x , t) as well as of those of their q-means on balls touching Γ. The results represent a further step in the extensions of those obtained by Varadhan and by Magnanini-Sakaguchi in the linear regime. [ABSTRACT FROM AUTHOR]

We establish good numerical estimates for a certain class of integrals involving sixfold products of Bessel functions. We use relatively elementary methods. The estimates will be used in the study of a sharp Fourier restriction inequality on the circle in a companion paper. [ABSTRACT FROM AUTHOR]

We study approximation properties of sequences of centered random elements X d , d ∈ N , with values in separable Hilbert spaces. We focus on sequences of tensor product-type and, in particular, degree-type random elements, which have covariance operators of a corresponding tensor form. The average case approximation complexity n X d ( ε ) is defined as the minimal number of continuous linear functionals that is needed to approximate X d with a relative 2-average error not exceeding a given threshold ε ∈ ( 0 , 1 ) . In the paper we investigate n X d ( ε ) for arbitrary fixed ε ∈ ( 0 , 1 ) and d → ∞ . Namely, we find criteria of (un) boundedness for n X d ( ε ) on d and of tending n X d ( ε ) → ∞ , d → ∞ , for any fixed ε ∈ ( 0 , 1 ) . In the latter case we obtain necessary and sufficient conditions for the following logarithmic asymptotics ln n X d ( ε ) = a d + q ( ε ) b d + o ( b d ) , d → ∞ , at continuity points of a non-decreasing function q : ( 0 , 1 ) → R . Here ( a d ) d ∈ N is a sequence and ( b d ) d ∈ N is a positive sequence such that b d → ∞ , d → ∞ . Under rather weak assumptions, we show that for tensor product-type random elements only special quantiles of self-decomposable or, in particular, stable (for tensor degrees) probability distributions appear as functions q in the asymptotics. We apply our results to the tensor products of the Euler integrated processes with a given variation of smoothness parameters and to the tensor degrees of random elements with regularly varying eigenvalues of covariance operator. [ABSTRACT FROM AUTHOR]

Asymptotic analysis and sign-changing bubble towers for Lane--Emden problems ... where p>1p>1 and Ω is a smooth bounded domain of ℝ². The aim of the paper is to analyze the asymptotic behavior of sign changing solutions of (εp) as p → ∞. Among other results we show, under some symmetry assumptions on Ω, that the positive and negative parts of a family of symmetric solutions concentrate at the same point, as p → ∞, and the limit profile looks like a tower of two bubbles given by a superposition of a regular and a singular solution of the Liouville problem in ℝ². [ABSTRACT FROM AUTHOR]

Consider a multiplicative function taking values on the unit circle. Is it possible that the partial sums of this function are bounded? We show that if we weaken the notion of multiplicativity so that for all primes p in some finite set P, then the answer is yes. We also discuss a result of Bronšteĭn that shows that functions modified from characters at a finite number of places must have unbounded partial sums. [ABSTRACT FROM AUTHOR]

The energy of a Von Kármán circular plate is described by a nonlocal nonconvex one-dimensional functional depending on the thickness ε. Here we perform the asymptotic analysis via Γ-convergence as the parameter ε goes to zero. [ABSTRACT FROM AUTHOR]

This article considers an amortized fixed rate mortgage where the borrower has the choice of prepayment. Asymptotic behaviors of the contract value are fully analyzed. Based on a known fact about the optimal prepayment boundary, two analytical approximations to the value of the mortgage contract are derived. Numerical experiments are carried out to validate the accuracy of the approximation formulas. In general, the relative error is less than 4%. [ABSTRACT FROM AUTHOR]

We consider single-carrier and single-user transmissions over a frequency-selective channel. We address the problem of joint estimation of the channel and the carrier frequency offset using a known training sequence (TS). Since in general the TS that is optimum for CFO estimation is not optimum for channel estimation, here we design the TS to minimize the mean-square error on the soft estimates of the data symbols obtained using a Wiener equalizer after CFO compensation. Our design results apply to the general scenarios of correlated and/or Ricean channel taps. Simulations measuring the bit error rate show an interesting gain when using the proposed training schemes in lieu of standard schemes. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the qualitative analysis, existence of equilibria and asymptotic behavior of some second-order models of the competition between tumor and immune cells. The background model belongs to d’Onofrio [A. d’Onofrio, A general framework for modeling tumor–immune system competition and immunotherapy: Mathematical analysis and biomedical inferences, Physica D 208 (2005) 220–235; A. d’Onofrio, Tumor–immune system interaction: Modelig the tumor-stimulated proliferation of effectors and immunotherapy, Math. Models Methods Appl. Sci. 16 (2006) 1375–1401]. Various developments proposed in this paper are focussed on the hiding–learning dynamics, followed by the qualitative analysis. [Copyright &y& Elsevier]

Abstract: This paper deals with a nonlinear parabolic equation with a more complicated source term, which is a product of localized source u q (0, t), local source u p (x, t), and weight function a(x). We investigate how the three factors influence the asymptotic behavior of solutions. It is shown that the blow-up set consists of single point {x =0} if p >1. When 0⩽ p ⩽1 with p + q >1, the blow-up take place everywhere in B. Moreover, the blow-up rate estimate is established with more precise coefficients determined. [Copyright &y& Elsevier]

In this paper, we study the Navier–Stokes and Euler equations in a domain with small depth. With this aim, we introduce a small adimensional parameter ε related to the depth. First we make a change of variable to a domain independent of ε and then we use asymptotic analysis to study what happens when ε becomes small. This way we obtain two new models for ε small that, after coming back to the original domain and without making a priori assumptions about velocity or pressure behaviour, give us a shallow water model including a new diffusion term (obtained from Navier–Stokes equations) and a shallow water model without viscosity and explicit dependence on depth (obtained from Euler equations). [Copyright &y& Elsevier]

Methods of weakly nonlinear theory are used in the present paper in order to study the development of instability in shallow water for the case where the flow is assumed to be slightly non-parallel. An asymptotic scheme where slow divergence of the base flow is taken into account is applied to shallow water equations with averaging coefficients. An amplitude evolution equation for the most unstable mode is derived. [ABSTRACT FROM AUTHOR]

This article reexamines the scope of a two-stage methodology for constructing a fixed-width confidence interval for the difference between two independent normal population means. We address directly the problem in a Behrens-Fisher situation, that is, when the variances of the two populations are both unknown and unequal. However, we show that the proposed methodology remains valid when the two variances are equal but unknown. We apply a two-stage procedure to the Behrens-Fisher situation using two approaches. In the first approach, we work with the differences of each observation in the first sample with all observations in the second sample. In the second approach, we work with the differences of paired observations from samples 1 and 2. Next, to overcome the problem of oversampling associated with the two-stage procedures, we apply the bootstrap methodology to modify the two-stage procedures. These methods, with and without bootstrapping, are compared with the help of a large-scale simulation study. [ABSTRACT FROM AUTHOR]

Numerical computations show that solutions of hyperbolic conservation laws obtained by second or higher order shock capturing methods in many cases are only first order accurate downstream of shocks (see, e.g., [M. H. Carpenter and J. H. Casper, AIAA J., 37 (1999), pp. 1072--1079]). We use matched asymptotic expansions to analyze the degeneration in order of accuracy for stationary solutions of hyperbolic conservation laws in two space dimensions. [ABSTRACT FROM AUTHOR]

This paper is a sequel to Part I (Trabelsi [11]) in which a new two-dimensional membrane model was derived via a formal asymptotic procedure for a family of hyperelastic nonlinear materials proposed by Ciarlet and Geymonat whose stored energy function is polyconvex and becomes infinite when the determinant of the deformation gradient tends to zero, and can be adjusted to arbitrary Lamé constants. Here, we continue the asymptotic analysis by making legitimate assumptions on the data to produce an inextensional two-dimensional model. [ABSTRACT FROM AUTHOR]

Abstract: The subject of this paper is the asymptotic analysis of a multi-structure made of two thin linearly elastic shells. It is assumed that the middle surfaces of the two shells are linked together on a part of their boundary, that at each point of their intersection, the two middle surfaces have distinct tangent planes and that the order of the applied body force density is , where ɛ is the half-thickness of each shell. We then identify the limit when ɛ tends to zero of the solution of the ‘scaled’ three-dimensional linearized elasticity problem. It is shown in particular that this limit is constituted of inextensional displacement fields for each shell and such that the junction is rigid (the angle between the middle surfaces of the two shells at the junction is unchanged by the deformation of the multi-structure). Moreover this limit is the same as the limit of the solution of the classical shell model (or Koiter model) for the multi-structure with the condition of rigid junction. [Copyright &y& Elsevier]

This work is devoted to the dynamical system (SRB): d (∂̸ h ( x ( t )))/ dt +∇ Φ ( x ( t ))∋ 0, with h a proper lower semicontinuous convex function. Existence and uniqueness of solutions are examined. Systems (SRB) include the class of gradient systems with respect to a Hessian Riemannian metric induced by a convex Legendre function h : . Moreover, class (SRB) is closed in a variational sense: links are made with regularized Lotka-Volterra systems and the limit equations obtained by letting the barrier parameter go to 0. Of particular interest is the case h ( x )= (1/2)| x | 2 +δ C ( x ): this way, one obtains a new gradient-projection method. System (SRB) bears a direct relation with the minimization of Φ over the domain of ∂̸ h ; the asymptotic behaviour of solutions, as time goes to infinity, is a real issue, which is addressed for a convex Φ and a h of the form h = k +δ C , with k convex and C a finite-dimensional polyhedron. [ABSTRACT FROM AUTHOR]

A relaxation system for the incompressible and compressible Euler and Navier-Stokes equations is considered. A numerical scheme working uniformly in the above limits is constructed using higher-order nonoscillatory upwind discretizations and higher-order implicit-explicit time discretization. Numerical results are presented for several test cases. [Copyright &y& Elsevier]

This article addresses some asymptotic and numerical issues related to the solution of Burgers' equation, -εuxx+ut+uux = 0 on (-1,1), subject to the boundary conditions u(-1) = 1+δ, u(1) = -1, and its generalization to two dimensions, -εΔu+ut+uux+uuy = 0 on (-1, 1)×(-π, π), subject to the boundary conditions u¦x=1 = 1 + δ, u¦x=-1 = -1, with 2π periodicity in y. The perturbation parameters δ and ε are arbitrarily small positive and independent; when they approach 0, they satisfy the asymptotic order relation δ = Os(e-a/ε) for some constant a ∈ (0,1). The solutions of these convection-dominated viscous conservation laws exhibit a transition layer in the interior of the domain, whose position as t → ∞ is supersensitive to the boundary perturbation. Algorithms are presented for the computation of the position of the transition layer at steady state. The algorithms generalize to viscous conservation laws with a convex nonlinearity and are scalable in a parallel computing environment. [ABSTRACT FROM AUTHOR]

Lower-order errors downstream of a shock layer have been detected in computations with nonconstant solutions when using higher-order shock capturing schemes in one and two dimensions [B. Engquist and B. Sjögreen, SIAM J. Numer. Anal., 35 (1998), pp. 2464­2485]. By analyzing the steady-state solution of slightly viscous hyperbolic systems of conservation laws we find that the solution can have an O(h)-dependence downstream of a shock layer, although the viscous term in that region is of O(h2). Numerical examples illustrate the analysis. [ABSTRACT FROM AUTHOR]

An asymptotic-induced scheme for nonstationary transport equations with the diffusion scaling is developed. The scheme works uniformly for all ranges of mean-free paths. It is based on the asymptotic analysis of the diffusion limit of the transport equation. A theoretical investigation of the behavior of the scheme in the diffusion limit is given and an approximation property is proven. Moreover, numerical results for different physical situations are shown and the uniform convergence of the scheme is established numerically. [ABSTRACT FROM AUTHOR]

Some techniques for solving recurrences are presented, along with examples of how these recurrences arise in the analysis of algorithms. In addition, probability generating functions are discussed and used to analyze problems in computer science. [ABSTRACT FROM AUTHOR]